非线性变形节理中纵波传播特性的理论研究

基于波前动量守恒理论和位移不连续方法所提出的时域分析新方法,引入岩石非线性法向本构关系,对弹性纵波在岩石非线性节理中的传播特性进行了理论分析。采用节理变形的双曲线模型(BB模型),获得纵波P波斜入射非线性节理的传播波动方程,并通过参数研究分析了在岩石节理中节理非线性系数、节理初始刚度、应力波入射角和入射波幅值等因素对纵波传播规律的影响。结果表明:所推导的应力波传播方程在考虑多种非线性问题时,通过迭代计算即可方便求出透射波和反射波的数值解,避免了复杂的数学运算;当波斜入射节理面时,产生了波型转换,节理变形的非线性对透射波和反射波有较大影响,透射系数和反射系数并非随着非线性参数的变化而单调变化。时域内所推导的波传播方程更有益于波斜入射时非线性参数的广泛研究,为开展该方面的理论研究工作提供了借鉴。     

层状弹塑性板动力变形的数值研究(英文)

本文研究了搁置在任意形状轴承上的层状平板,加上脉冲载荷(如炸药爆炸),结果产生塑性流动,改变了板和轴承的接触和破坏了层状板之间的接合,使之发生滑移,最后板形成残余形变,强动载冲击板产生形变的实际过程可分为两个阶段:第一阶段为应力波的传播和在板内应力波的相互作用,主要是从自由面反射的应力波和从轴承面反射的应力波,波经重复几次反射后,造成板的屈曲状态,其间,板的中间层始终保持中线弹性状态。第二阶段为板内某些截面发生塑性形变,随厚度不同而不同地收缩,同时所有的板均拉伸而增加了板的弯曲,最后,塑性形变消耗掉能量后,板各单元变为弹性状态而产生某种模型的振动。     

密度梯度柱壳链的弹性波传播特性研究

均匀圆柱壳链可以调控弹性波传播, 引入密度梯度有望进一步提高波形调控能力. 通过建立密度梯度柱壳链的细观有限元模型和连续介质模型, 研究了密度梯度柱壳链的弹性波传播特性. 通过将密度梯度柱壳链等效为变密度连续介质弹性杆, 建立了其在应力脉冲作用下的控制方程. 运用拉普拉斯积分变换方法, 考虑杆中密度遵循线性分布, 获得了方程的解析解. 以三角形应力脉冲作用为例, 通过与细观有限元模拟结果比较, 发现解析解可以较好地预测梯度柱壳链中载荷的演化趋势. 正梯度链中载荷峰值随着波传播逐渐增大, 负梯度链中载荷峰值随着波传播逐渐减小. 正梯度链支撑端峰值载荷高于均匀链, 负梯度链支撑端峰值载荷低于均匀链, 这表明相较于均匀柱壳链, 密度梯度柱壳链可以在更大范围内对波形进行调控. 线性密度梯度参数对梯度柱壳链的波形调控能力影响较大, 梯度参数越小, 传递到支撑端的峰值载荷越小; 相反, 梯度参数越大, 支撑端的峰值载荷越大. 建立的理论模型及其解析解为研究梯度柱壳链中应力波传播规律及揭示载荷调控机理提供了理论基础.      

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。     

基于Lord-Shulman理论的热弹性波在偶应力三明治固体中的反射和透射

在温度急剧变化、短时间极速加热等极端情况下，基于Fourier定律的热流矢量与温度梯度成正比关系的经典热传导理论不能准确描述其物理过程．经典热弹性理论的热传导方程是抛物型的，而广义热弹性理论包含双曲型方程，热将以具有有限传播速度的波动形式传播．本文基于Lord-Shulman广义热弹性理论和修正偶应力弹性理论，得到在偶应力热弹性固体中四种色散波，研究热弹性波的传播和在偶应力固体三明治结构中的反射透射问题，重点研究横波入射时偶应力参数和热弛豫时间对各种热弹性耦合波反射透射系数的影响．     

结构中弹性波传播的可视化方法

由于结构中弹性波传播的复杂性，其场量(位移、应变、速度)表达式往往为繁杂、冗长的数学表达式，表达式本身不能直观、形象地表征结构中弹性波的传播特征．本文以杆中纵波传播为例，基于Matlab开发了弹性波传播特征的可视化程序，将杆中纵波传播特性以一种动态、直观、形象的形式展现出来．     

弯曲波彩虹捕获效应及其在能量俘获中的应用

弹性波在色散关系经过设计的梯度结构中传播时会产生空间分频现象和波场能量增强现象, 即不同频率的弹性波会在结构的不同位置停止向前传播并发生能量聚集, 这就是弹性波彩虹捕获效应. 其相关研究成果可以促进结构健康监测、振动控制以及能量俘获等领域的发展. 本文通过所设计的梯度结构梁, 系统地研究了弯曲波彩虹捕获效应及其在压电能量俘获中的应用. 首先, 利用传递矩阵法获得了梯度结构梁元胞能带结构的解析解, 进而分析了弯曲波彩虹捕获效应的产生机理: 不同频率的弯曲波会在不同元胞附近群速度减小到零, 从而停止向前传播并发生反射; 入射波和反射波的叠加, 以及群速度减小带来的能量聚集, 会显著增强反射处的波场能量. 其次, 通过有限元仿真和实验验证了弯曲波彩虹捕获效应的空间分频现象和波场能量增强现象. 最后, 通过有限元多物理场耦合仿真和实验, 研究了粘贴PVDF压电薄膜的梯度结构梁相对于均匀梁的弯曲波能量俘获效果及其随入射波频率的变化规律. 结果表明, 在弯曲波彩虹捕获效应发生频带内, 粘贴在梯度结构梁上的PVDF压电薄膜的输出电压约为粘贴在均匀梁相应位置处的PVDF压电薄膜的输出电压的2倍.      

椭圆柱壳链的波形弥散特性研究

椭圆柱壳链可以引起波形弥散，从而可以调控应力波的传播.本文通过3D打印、冲击测试、细观有限元模拟和理论分析，研究了在质量块冲击加载下，单胞纵横比、冲击质量和速度对椭圆柱壳链中弹性波传播弥散行为的影响.结果表明，冲击过程中，椭圆柱壳链结构中的速度峰值随着波传播逐渐减小，纵横比越大或冲击质量越小，速度峰值衰减越剧烈，而冲击速度对椭圆柱壳链的波形弥散行为几乎无影响.相关研究对新型波形控制器的设计和精确有效地调控弹性波传播具有重要意义.     

理想直杆中轴向应力波的传播和反射导致的分叉问题

对阶跃载荷作用下弹性理想完善直杆中应力波的传播及其反射引起民的分叉问题进行了理论分析和数值计算，讨论了此类动力屈曲问题中横向惯性效应的影响；给出了一种进行后分叉分析的近似方法，得到了一些结论，在各类结构由于应力波的传播及反射引起的分叉问题具有指导意义。     

爆炸载荷下脆性颗粒体系破碎特性的数值研究

试验发现,以球形TNT为中心爆源,球形玻璃珠构成的颗粒和球壳中发生破碎的颗粒体积分数随当量比(颗粒球壳的质量与TNT炸药的质量比)的增加呈现指数衰减规律。采用有限元与离散元耦合的连续非连续数值方法,揭示了中心炸药起爆后颗粒环壳内爆炸波的传播衰减和在环壳外界面反射后的稀疏卸载过程。由于爆炸波的短脉冲特性,颗粒内部应力场始终处于应力非均衡状态,采用应力均衡状态下颗粒破碎强度的Weibull分布会得到远高于试验测得的破碎颗粒体积分数。因此采用破坏波传播特征时间内的平均诱导应力而非瞬时诱导应力作为颗粒破碎强度的应力指标,并通过试验结果确定破坏波传播特征时间。考虑了应力传播的非均匀性对于颗粒破碎的影响,得到了平均诱导应力峰值的概率分布随比例距离的变化规律,结合修正后的颗粒破碎强度Weibull分布建立了破碎颗粒体积分数随比例距离的变化模型。     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.     

有限长Timoshenko梁弹性碰撞接触瞬间的动态特性

给出了质点与有限长Timoshenko梁横向弹性碰撞接触问题的半解析解,分析了该碰撞问题在碰撞接触瞬间的动态响应特性：揭示了其中的波传播现象．     

Influence of prestress on the velocities of plane waves propagating normally to the layers of nanocomposites

The paper is concerned with longitudinal and transverse waves propagating at a right angle to the layers of a nanocomposite material with initial (process-induced residual) stresses. The composite consists of alternating layers of two dissimilar materials. The materials are assumed nonlinearly elastic and described by the Murnaghan potential. For simulation of wave propagation, a problem is formulated within the framework of the three-dimensional linearized theory of elasticity for finite prestrains. It is established that the relative velocities of waves depend linearly on small prestresses. In some composite materials, however, the thicknesses of the layers may be in a ratio such that the wave velocities are independent of the prestress level __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 3–22, July 2006.     

超声纯横波法测试45#钢的内部应力

声各向同性的金属材料在应力作用下,材料表现出声各向异性,这是用声弹性法分析材料内部应力的基础。本文用垂直于应力方向传播的超声纯横波对45#钢进行测试,测试时横波的偏振化方向分别平行和垂直于应力方向。实验结果表明:材料在拉、压应力作用下,相互正交的两超声纯横波的声速都发生了变化,且声各向异性因子与应力成线性关系。利用此关系可测试材料内部应力,提供了一种无损测试材料内部应力的方法,另外本实验方法也可以对材料内部残余应力进行评估。实验中利用回振法测量声速,可测量声速的微小变化,精度高。     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

Submerged fluid-filled cylindrical shell subjected to a shock wave: Fluid–structure interaction effects

A submerged fluid-filled circular cylindrical shell subjected to a shock wave propagating in the external fluid is considered. The study focuses on a number of acoustic and structural effects taking place during the interaction. Specifically, the influence of the acoustic phenomena in the fluid on the stress–strain state of the shell is analysed using two different visualization techniques. The effect that the parameters of the shell have on the internal acoustic field is addressed as well, and the ‘shock transparency’ of various shells is discussed. Special attention is paid to the analysis of the contribution of the terms in the shell equations representing bending stiffness, and the limits of applicability of the membrane theory of thin shells are discussed in the fluid–structure interaction context. The possibility of cavitation in the internal fluid is investigated, and the effect that cavitation could have on the structural dynamics of the shell is discussed. The present paper is a follow-up of the author's earlier study of the interaction between fluid-filled cylindrical shells and external shock waves.     

Interesting effects in harmonic generation by plane elastic waves

The harmonics of plane longitudinal and trans-verse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a pri-mary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.     

Multiple fractures produced by the bending of brittle beams

This paper describes experiments where the bending of beams results in two or more fractures being formed, apparently simultaneously. This is explained in terms of the stress waves emitted by the initial fracture process. It is shown that three separate types of secondary fracture may occur as a result of the interaction between the stress pulses produced by the initial fracture and the loading stresses already present in the beam. In treating these problems it has been found helpful to use an analytical solution for the bending wave propagated when a semi-infinite beam, which is subjected to a constant bending moment, is suddenly unloaded at the free end. In modelling the longitudinal stress pulse produced by the fracture we have used a simplified model which assumes that the forcing function on the fracture plane is a force field equal to the resultant force acting on the unbroken portion of the fracture surface prior to the onset of fracture.     

Intense bending waves in a bar

Summary In this paper, the work presented in [1] is extended to study higher-order approximations of nonlinear effects in a bar. It has been found that long bending waves, being the low-frequency modes involved in resonant triads, are stable against small perturbations. Consequently, a bending wave with group velocity which is less than that of longitudinal waves should behave as a linear quasi-harmonic wavetrain. On the other hand, one may expect self-modulation instability of intense bending wavetrains during the long-time evolution. This paper overcomes such a contradiction. To describe the nonlinear dynamics in detail, one should allow for higher-order approximation effects in the model. Such effects are associated with the diffusion of linear wave packets due to different group velocities, and amplitude dispersion caused by nonlinearity. Within the second-order approximation analysis, an amplitude modulation is indeed experienced for intense bending waves. As a result, envelope solitons can be formed from unstable bending wavetrains. The group matching of long longitudinal and short bending waves, being a particular case of the self-modulation, is of special interest as a limit case of the triple-wave resonant interactions. It demonstrates the relation between the first- and the second-order approximation effects. Accepted for publication 20 July 1996